Bars and rod

Two cylindrical horizontal bars are fixed one above the other; the distance between the axes of the bars is \(\ 4d \), where \(\ d \) is the diameter of the rod. Between the bars, a cylindrical rod of diameter \(\ d \) is placed as shown in Figure (this is a vertical cross-section of the system). The coefficient of friction between the rod and the bars is \(\ ยต = 1/2 \). If the rod is long enough, it will remain in equilibrium in such a position. What is the minimal length \(\ L \) of the rod required for such an equilibrium?

You can express your answer in the form \(\ L=xD \), where \(\ x \) is a positive, real number. Find \(\ x \).

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